Refusing to allow members of their squad to represent Germany would leave Bayern open to sanctions.
Under FIFA regulations, clubs are obliged to release players to national teams during international windows and major tournaments.
Neuer, 33, has captained Germany since September 2016.
The Schalke product missed much of the 2017-18 season through injury, enabling Ter Stegen to deputise, but returned in time for the World Cup in Russia and has started each of Germany's six matches in 2019.